Find the inverse of the relation {(1, 0), (3, -8), (4, -3), (7, -5), (9, -1)}

To find the inverse of a relation, we swap each ordered pair's \( x \)-coordinate and \( y \)-coordinate. The inverse of the relation \( R = \{(1, 0), (3, -8), (4, -3), (7, -5), (9, -1)\} \) is obtained by flipping the pairs.

Here’s the process:

- The inverse of \( (1, 0) \) becomes \( (0, 1) \)
- The inverse of \( (3, -8) \) becomes \( (-8, 3) \)
- The inverse of \( (4, -3) \) becomes \( (-3, 4) \)
- The inverse of \( (7, -5) \) becomes \( (-5, 7) \)
- The inverse of \( (9, -1) \) becomes \( (-1, 9) \)

Thus, the inverse of the given relation is:
\[
R^{-1} = \{(0, 1), (-8, 3), (-3, 4), (-5, 7), (-1, 9)\}
\]

Would you like further explanation or have any questions?

Here are 5 related questions to extend your understanding:

1. What does it mean for a relation to have an inverse?
2. How do you determine if a relation is a function?
3. Is the inverse of a function always a function? Why or why not?
4. Can you graph both the relation and its inverse to visualize the process?
5. How do you determine if an inverse relation is also a function?

**Tip:** For a function to have an inverse function, it must be both one-to-one (injective) and onto (surjective).

Learn how to find the inverse of a relation with ordered pairs such as {(1, 0), (3, -8), (4, -3), (7, -5), (9, -1)}. This step-by-step solution explains how to swap the x- and y-coordinates of each pair to find the inverse. Suitable for students in Grades 9-10.

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